The TGFT of the form \(T^6_5\)  on the \(U(1)\)  group with closure constraint is proved to be renormalizable [1]}. The proof of this claim is performed using multi-scale analysis. The closure constraint also called gauge invariance condition can help to define the emergence of the metric on spacetime after phase transition and therefore makes this type of model relevant for the understanding the quantum theory of gravitation. This kind of model with closure constraint namely the six dimensional TGFT with quartic interactions is studied recently in [2]} and [3]}. The perturbative computation of the \(\beta \) -functions of the \(T^6_5\)  model is given in [4]}, in which, we have showed that this model is asymptotically free in the UV. This result seems to be non consistant in the point of view of the FRG analysis.
This paper aims at giving the FRG analysis to a renormalizable tensor model \(T^6_5\)  with closure constraint and for improving the conclusion given in [4]}. In a truncation containing all relevant and marginal interactions, we find nontrivial fixed points. The FRG flows for coupling constants and for the mass parameter are solved
numerically.
